Differentiate y=x^2+bx+c, and hence find b and c if: the parabola has y-intercept and has gradient -2 there?

1 Answer
Jun 4, 2018

# b = -2 #

There is insufficient information to find #c#

Explanation:

We have a Parabola with equation # y = x^2 + bx + c # and tangent gradient #-2# at the #y#-intercept:

Differentiating wrt #x# we get:

# y' = 2x+b #

The tangent has gradient #-2# at the #y#-intercept, thus:

# y'(0) = -2 => 2(0)+b = -2 => b = -2 #

Thus we can write the equation:

# y = x^2 - 2x + c #

There is insufficient information to find #c#